On componentwise error estimates for inverse matrices

Abstract

LetA be an×n-matrix with the property ‖I−A‖<1. LetY be an approximation of the inverse ofA. This paper shows how to get a componentwise error estimate forY, that does not require too much numerical effort but generally presents better results than global error estimates do. Although proved by means of interval mathematics, the given error estimate can also be calculated in absence of any implementation of interval arithmetic.